Completion Problems First¶

Strategy · All strategies
Evidence · 8 claims (5 for, 1 mixed, 2 against) · 14 studies (6 causal, 4 review, 2 quant-synthesis, 2 theoretical), q1–q4 · 1 of 14 report an effect size · 2 claims rest on one study

Description¶

Completion problems first is a sequencing strategy in which learners' earliest practice tasks are partially completed — some steps or solution states are given, and learners fill in the remainder. It operationalizes the completion strategy (van Merriënboer) as a bridge between studying full worked examples and solving problems unaided, implementing a smooth fading of guidance rather than an abrupt transition.

Design Implications¶

Completion problems reduce the unguided search that makes early problem solving inefficient for novices, while requiring more generative processing than passive example study Worked examples reduce unnecessary search for novices. [+M]. Because learners must actively complete steps, the strategy avoids the shallow encoding and illusion of understanding that full-example study alone can produce Example-based sequences outperform problem-only practice for novices, and fading support is argued to aid transfer [+S]. The design task is choosing which steps to omit: omit steps that isolate the goal-rule or decision being taught, and fade progressively as performance improves.

Context¶

Requirements¶

• A set of high-quality worked examples establishing the full solution procedure first
• A task sequence that fades support: full example → completion problem (most steps given) → completion problem (few steps given) → full problem (Fading)
• Deliberate selection of which steps to blank — typically the steps carrying the learning goal, not arbitrary gaps
• Feedback or a correct model answer so learners can check their completions
• A set of high-quality worked solutions to draw the completed portion from
• A task sequence in which the completed portion shrinks (and learner-supplied portion grows) as competence develops (Fading [+M])
• Clear marking of which steps are given and which the learner must supply, so learners do not waste effort parsing the interface rather than the content
• Feedback or a correct final solution available for self-checking after completion

Constraints¶

• If too many steps are omitted too early, learners revert to inefficient search strategies and cognitive overload Cognitive overload degrades learning. [-M]
• Blank steps that are trivial (e.g., routine arithmetic) add workload without promoting schema construction [~M]
• For learners with substantial prior knowledge, completion scaffolds become redundant and slow performance Worked-example guidance becomes less effective as learner expertise increases. [~M]
• Without a model answer to compare against, learners may consolidate incorrect completions [-M]
• For learners with high prior knowledge, the provided portion is redundant and adds extraneous load rather than reducing it Guidance becomes less effective — and can reverse in benefit — as expertise grows. [-M]
• Poorly aligned given/learner portions (e.g., giving the conceptually hard steps and asking for mechanical ones) undermine the intended scaffolding
• In ill-structured domains with no canonical solution path, a "partial solution" may mislead learners about the nature of the task

Implementation Variability¶

• Backward fading: remove the last steps first (learners finish solutions), then earlier steps — common in mathematics tutoring
• Forward fading: remove early steps first, forcing learners to plan before executing
• Completion within worked-example pairs: alternate example study with an isomorphic completion problem (example–problem pairs)
• Programmatic fading: in adaptive systems such as ASSISTments or Squirrel AI, the number of given steps adjusts to learner performance
• Forward fading: start with a full worked example, then completion problems with decreasing support, then full problems — the classic sequence (Renkl & Atkinson, 2003)
• Backward fading: begin with completion problems where only the final step is missing, then fade earlier steps in; some evidence suggests fading later steps first benefits learners with weaker prior knowledge [~M]
• Alternation: interleave worked examples and isomorphic problems one-to-one rather than using completion problems as the intermediate form
• Error-based variants: the given portion contains a deliberate error the learner must find and fix Erroneous examples can build conceptual knowledge by prompting learners to explain and correct flawed solutions. [+W]

Target Learners¶

• Novices who lack the schemas to benefit from unguided problem solving Worked examples reduce unnecessary search for novices. [+M]
• Learners who have studied worked examples but are not yet ready for independent problems
• Less appropriate for advanced learners, who perform better solving problems directly Worked-example guidance becomes less effective as learner expertise increases. [~M]
• Novices in a structured domain (algebra, programming, physics, statistics) who would otherwise flounder in unguided search Example–problem sequences reduce cognitive load for novices. [+M]
• Intermediate learners transitioning from example study to independent problem solving

Target Learning Goals¶

• Procedural skill acquisition in well-structured domains (algebra, programming, statistics)
• Schema construction for recurring problem types
• Bridging toward transfer: faded completion supports application to novel variants Example-based sequences outperform problem-only practice for novices, and fading support is argued to aid transfer [+S]
• Procedural skill acquisition: executing the steps of a well-defined solution method
• Schema construction: internalizing the structure of a problem type so full solutions are no longer needed
• Self-explanation and monitoring: noticing what the given steps accomplish and why the remaining steps follow

Instructions¶

1. Present a fully worked example with reasoning made visible (Think-Aloud or annotated steps).
2. Assign a completion problem on an isomorphic task with the goal-critical steps blanked; provide the completed example alongside for reference (Worked Examples).
3. Fade: progressively blank more steps across successive tasks (Fading), monitoring accuracy (Check-In).
4. Transition to full problem solving once completion accuracy is high, with feedback on each attempt (Practice, Assessment).

Related Strategies¶

• Worked examples first — the preceding phase; completion problems assume example study has occurred
• Faded guidance — the general principle this strategy instantiates in problem sequences
• Example-problem pairs — an alternating variant with similar rationale
• Design AI educational systems that fade support and require learner justification to preserve independent problem solving
• Problem-Based Learning — the contrast case: minimal guidance, appropriate only after schemas are established
• Scaffolded Practice — completion problems are a form of scaffolded practice with the scaffold defined by solution completeness
• Fade embodied support as schemas develop, starting with the least embodied task-relevant support

Examples¶

• van Merriënboer's 4C/ID task sequences — complex-skill curricula (e.g., technical training) begin each task class with completion tasks and fade to conventional tasks (Four-Component Instructional Design)
• Khan Academy — hint sequences effectively function as on-demand completion problems, revealing solution steps one at a time
• Renkl & Atkinson's fading studies — algebra tutoring sequences that faded worked examples into completion problems and then full problems, improving near transfer
• van Merriënboer's programming curriculum (LOGO and Pascal studies) — learners completed partially written programs rather than writing programs from scratch, producing better learning with less invested effort than generation from scratch.
• Khan Academy (https://www.khanacademy.org) — its exercise hint system progressively reveals solution steps; a learner who takes the first hint is effectively working a completion problem.
• Codecademy (https://www.codecademy.com) — early exercises provide scaffolded code with TODO gaps the learner fills, fading toward free-form projects.
• Math Academy (https://www.mathacademy.com) — diagnostic-prescribed problem sequences that move from heavily supported items to independent problems as mastery evidence accumulates.

Key Sources¶

• van Merriënboer, J. J. G. (1990). Strategies for programming instruction in high school: Program completion vs. program generation. Journal of Educational Computing Research, 6(3), 265–285. doi:10.2190/NW2X-L8GK-M8PP-1L7N
• Renkl, A., Atkinson, R. K., & Große, C. S. (2004). How fading worked solution steps works — a cognitive load perspective. Instructional Science, 32(1–2), 59–82. doi:10.1023/b:truc.0000021815.74806.f6
• van Merriënboer, J. J. G., & Kirschner, P. A. (2018). Ten steps to complex learning (3rd ed.). Routledge.
• Sweller, J., van Merriënboer, J. J. G., & Paas, F. (2019). Cognitive architecture and instructional design: 20 years later. Educational Psychology Review, 31(2), 261–292. doi:10.1007/s10648-019-09465-5
• Paas, F., & van Merriënboer, J. J. G. (1994). Variability of worked examples and transfer of geometrical problem-solving skills: A cognitive-load approach. Journal of Educational Psychology, 86(1), 122–133. doi:10.1037/0022-0663.86.1.122
• Renkl, A., & Atkinson, R. K. (2003). Structuring the transition from example study to problem solving in cognitive skill acquisition: A cognitive load perspective. Educational Psychologist, 38(1), 15-22. doi:10.1207/s15326985ep3801_3